Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
Probabilistic Reasoning Under Coherence in System P
Annals of Mathematics and Artificial Intelligence
Generalizing inference rules in a coherence-based probabilistic default reasoning
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Quasi conjunction, quasi disjunction, t-norms and t-conorms: Probabilistic aspects
Information Sciences: an International Journal
Conditional random quantities and iterated conditioning in the setting of coherence
ECSQARU'13 Proceedings of the 12th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
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We study in the setting of probabilistic default reasoning under coherence the quasi conjunction, which is a basic notion for defining consistency of conditional knowledge bases, and the Goodman & Nguyen inclusion relation for conditional events. We deepen two results given in a previous paper: the first result concerns p-entailment from a finite family F of conditional events to the quasi conjunction C(S), for each nonempty subset S of F; the second result analyzes the equivalence between p-entailment from F and p-entailment from C(S), where S is some nonempty subset of F. We also characterize p-entailment by some alternative theorems. Finally, we deepen the connections between p-entailment and inclusion relation, by introducing for a pair (F,E|H) the class of the subsets S of F such that C(S) implies E|H. This class is additive and has a greatest element which can be determined by applying a suitable algorithm.